Yes. We offer free domain privacy.
You can set it by logging into your billing account -> Domains -> Expand the domain in question by clicking the + (plus) sign -> Private Registration -> Turn On/Off
**EDIT July 13, 2015**
Starting July 13, 2015 domain private registration is no longer a free offering by Arvixe. Effective immediately, domain privacy is now an addon option in the checkout offered at $9.99/yr for a single domain. For existing customers with private registration enabled on domains that were registered before 7/13/2015 will be considered legacy customers. Those domains with private registration already enabled will remain free as long as you remain an Arvixe customer.